Scalability analysis of multidimensional wavefront algorithms on large-scale SMP clusters

We develop a model for the parallel performance of algorithms that consist of concurrent, two-dimensional wavefronts implemented in a message passing environment. The model combines the separate contributions of computation and communication wavefronts. We validate the model on three supercomputer systems, with up to 500 processors, using data from an ASCI deterministic particle transport application, although the model is general to any wavefront algorithm implemented on a 2-D processor domain. We also use the model to make estimates of performance and scalability of wavefront algorithms on 100-TFLOPS computer systems expected to be in existence within the next decade. Our model shows that on a 1-billion-cell problem, single-node computation speed (nor inter-processor communication performance, as is widely believed) is the bottleneck. Finally, we present preliminary considerations that reveal the additional complexity associated with modeling wavefront algorithms on reduced-connectivity network topologies, such as clusters of SMPs.